The current measurements are performed near the electroweak scale \(Q\sim v\) . If the new physics scale \(\Lambda \)  is significantly larger than the energy probed at the LHC, the BSM effects generally scale as \((Q/\Lambda )^n\)  with \(n\ge 0\)  [1]}, [2]}, [3]}, before reaching a new resonance. Therefore, it is desirable to enhance the new physics effects by exploring the high energy regime associated with the Higgs physics.
Proposals have been made recently to study the off-shell Higgs signals \(gg \rightarrow h^*\rightarrow VV\)  [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. This process could be sensitive to potential new physics of the \(tth^*\)  and \(VVh^*\)  interactions or an \(h^*\)  propagation at high energy scales \(Q > v\) .
